No - everything saves automatically! You’re good to go. If you want to double check that your progress has saved, you can check the sync indicator in the header of your course.
If the sync indicator displays a green checkmark, everything has saved. If you see a red exclamation point, some progress hasn't synced yet. It will sync automatically, but you can also force the sync to happen immediately by clicking on "Sync Now."
You'll see a syncing icon when a sync is in progress: